Check original Play! Framework migration documentation first.
a) change Play! version from
    <properties>
        ...
        <play2.version>2.3.10</play2.version>
    </properties>
to
    <properties>
        ...
        <play2.version>2.4.11</play2.version>
    </properties>
b) remove repository definition (all artifacts are in Maven central repository)
    <repositories>
        <repository>
            <id>typesafe</id>
            <name>Typesafe - releases</name>
            <url>http://repo.typesafe.com/typesafe/releases/</url>
            <snapshots>
                <enabled>false</enabled>
            </snapshots>
        </repository>
    </repositories>
c) add dependency
        <dependency>
            <groupId>com.typesafe.play</groupId>
            <artifactId>play-netty-server_2.10</artifactId>
            <version>${play2.version}</version>
            <scope>runtime</scope>
        </dependency>
d) if enhancing classes, add dependency
        <dependency>
            <groupId>com.typesafe.play</groupId>
            <artifactId>play-enhancer</artifactId>
            <version>${play2-enhancer.version}</version>
        </dependency>
where play2-enhancer.version property needs to be added to project properties
    <properties>
        ...
        <play2-enhancer.version>1.1.0</play2-enhancer.version>
    </properties>
e) if using Specs2 tests add dependency
        <dependency>
            <groupId>com.typesafe.play</groupId>
            <artifactId>play-specs2_2.11</artifactId>
            <version>${play2.version}</version>
            <scope>test</scope>
        </dependency>
and repository definition
    <!-- 'com.typesafe.play:play-specs2_2.11' depends on
         'org.scalaz.stream:scalaz-stream_2.11:0.7a:jar'
         and this artifact is not available in Maven central repository yet,
         see https://github.com/scalaz/scalaz-stream/issues/258 -->
    <repositories>
        <repository>
            <id>scalaz-bintray</id>
            <name>Scalaz Bintray - releases</name>
            <url>https://dl.bintray.com/scalaz/releases/</url>
            <snapshots>
                <enabled>false</enabled>
            </snapshots>
        </repository>
    </repositories>
f) if using JDBC evolutions add dependency
        <dependency>
            <groupId>com.typesafe.play</groupId>
            <artifactId>play-jdbc-evolutions_2.11</artifactId>
            <version>${play2.version}</version>
        </dependency>
g) if using Ebean change
        <dependency>
            <groupId>com.typesafe.play</groupId>
            <artifactId>play-java-ebean_2.11</artifactId>
            <version>${play2.version}</version>
        </dependency>
to
        <dependency>
            <groupId>com.typesafe.play</groupId>
            <artifactId>play-ebean_2.11</artifactId>
            <version>${play2-ebean.version}</version>
        </dependency>
where play2-ebean.version property needs to be added to project properties
    <properties>
        ...
        <play2-ebean.version>1.0.0</play2-ebean.version>
    </properties>
and change plugin’s configuration parameter from
<serverJvmArgs>-DapplyEvolutions.default=true</serverJvmArgs>
to
<serverJvmArgs>-Dplay.evolutions.db.default.autoApply=true</serverJvmArgs>